There is increasing interest in developing wind powered generator systems in which electricity produced by a single wind powered generator or a group of wind powered generators can be supplied to utility power grids. A conventional wind turbine for generating electric power includes two or more turbine blades or vanes connected to a central hub. The hub rotates about a horizontal axis and is connected to a shaft that drives an electric power generator. Wind turbines operate at either a constant rotational speed despite changes in wind velocity or at variable rotational speeds that are proportional to the wind velocity. Peak power at high wind speeds is usually controlled through stall regulation or through the use of variable pitch turbine blades.
The portion of the turbine blade closest to the hub is called the root of the blade, and the portion of the turbine blade farthest from the hub is called the tip of the blade. A cross-section of a turbine blade taken perpendicular to the imaginary line connecting the blade's root to the blade's tip is generally referred to as an airfoil. Theoretically, each turbine blade includes an infinite number of airfoils along the imaginary line. However, a blade's shape is more practically defined in reference to a finite number of the airfoil shapes. In this regard, the geometric shape of an airfoil is usually expressed in tabular form in which the x, y coordinates of both the upper and lower surfaces of the airfoil at a given cross-section of the blade are measured with respect to the chord line, which is an imaginary line connecting the leading edge of the airfoil and the trailing edge of the airfoil. Both x and y coordinates are expressed as fractions of the chord length.
Another important parameter of an airfoil is its thickness. The thickness of an airfoil refers to the maximum distance between the airfoil's upper surface and the airfoil's lower surface and is generally provided as a fraction of the airfoil's chord length. For example, a fourteen percent thick airfoil has a maximum thickness (i.e., a maximum distance between the airfoil's upper surface and the airfoil's lower surface) that is fourteen percent of the airfoil's chord length. The chord length of an airfoil or cross-section of a turbine blade will typically become larger if the length of the blade increases and will typically become smaller if the length of the blade becomes smaller. Therefore, a table of coordinates for the geometry of the upper and lower surfaces of an airfoil remain valid for blades of different lengths because the coordinates are dimensionless and are provided as percentages of the chord length of the airfoil.
Another important parameter for every airfoil or blade cross-section is its operating Reynolds number. The Reynolds number of an airfoil at a particular radial station is dimensionless and is defined by the following equation: R=cV/ν where “R” is the Reynolds number, “c” is the chord length of the airfoil, “ν” is the flow velocity relative to the blade at the corresponding radial point on the blade, and “ν” is the kinematic viscosity of the air. Physically, the Reynolds number can be thought of as the ratio of the inertial force to the viscous force of air flow around a turbine blade. Viscous force is proportional to the shearing stress in the air flow divided by the rate of shearing strain, and inertial force is proportional to the product of the mass of the air flow multiplied by its acceleration. In practice, airfoil performance characteristics are expressed as a function of the airfoil's Reynolds number. As the length of a blade decreases, the blade's Reynolds number lends to decrease. For a particular airfoil along the blade span, a small Reynolds number indicates that viscous forces predominate while a large Reynolds number indicates that inertial forces predominate.
Conversion of wind power into electrical power is accomplished in most wind powered systems by connecting a wind-driven turbine to the shaft that drives an electric generator. An important concern for the wind power industry is mitigating rotor noise. Airfoil induced noise can be caused by a number of operating conditions or design characteristics including noise caused by inflow turbulence interaction with the leading edge of the blade or airfoil, noise associated with airfoil thickness effects, airfoil generated laminar separation bubbles, and noise generated by boundary layer interaction with the trailing edge of the blade or airfoil. Many consider the noise associated with the trailing edge to be the most significant. Aerodynamic noise sources can be obstacles to commercialization of both large and small wind turbines, and when these noise sources are not taken into account it is difficult to obtain a balance between airfoil performance and noise mitigation. In general, good airfoil performance and low noise coincide.
However, to date, airfoil designers have primarily concentrated on achieving good performance characteristics with their airfoil design with little or no consideration given to reducing noise. Significantly, the design process of airfoils for small machines or wind turbines, with Reynolds numbers on the order of 500,000, is quite different from the design of airfoils for very large machines or wind turbines, with Reynolds numbers on the order of 4,000,000 or larger. For small wind turbines, performance degradation and noise from laminar separation bubbles is of greater concern, but most best practice airfoil design was performed for larger machines and then simply transferred to the small machines which can result in reduced overall performance and increased noise.
Another concern for of wind turbine designers is providing a desired stiffness of the blades. Thick blade root airfoils are typically desirable for greater blade stiffness and high natural frequency placement. Blade stiffness increases in proportion to the airfoil thickness squared. Blades with a thick inboard region are more stable against buckling and a thick inboard region also reduces material requirements. However, airfoil drag increases with airfoil thickness along with an increase in the airfoil's sensitivity to roughness, which increases as the blade get coated with dirt, bugs, and other airborne contaminants. Additionally, greater airfoil thickness results in greater air displacement and associated noise.
Hence, there remains a need for families of improved airfoils to shape and condition the local airflow around blades for more efficient operation and wind power conversion to mechanical or electric power. Preferably, such airfoil families would be suitable for use with small and large wind turbines and would provide a desirable balance between the need for a quiet and stiff blade that also provides high performance, e.g., provide a desired balance between blade thickness, noise control, and airfoil performance.